Math Help - Finding Average values

1. Finding Average values

1. Find the average value of :
on the interval

Work: I know the formula is 1/(b - a) * ∫ f(x) dx (from x=a to b).

so I got (1/ (13pi/6))

Integrated 4sinx+7cosx= 4-cosx+7sinx, plugged in (13pi/6) and also 0 and subtracted them.

((13pi/6))[((4-cos((13pi/6))+7sin((13pi/6))))-((4-cos(0)+7sin(0)))]

But that is wrong...

2.find the average value of on the interval

same as above, it is (1/1)* integral of cos^4xsinx [from 0 to 1]
intregal of cos^4xsinx =(3+4cos(2x)+cos(4x))/8 -cosx

(3+4cos(2)+cos(4))/8*-cos1-(3+4cos(0)+cos(0))/8*-cos0

2. Originally Posted by softballchick
1. Find the average value of :
on the interval
Note that $\int {4\sin (x) + 7\cos (x) = - 4\cos (x) + 7\sin (x)}$
Did you divide by $\frac{13\pi}{6}~?$

3. thanks! Silly mistake, I multiplied it by 13pi/6 instead of 1/(13pi/6)